I’m gradually absorbing John Wesson’s wonderful book on Tokamaks, and wanted to share a sketch on safety factors.
A major factor in determining plasma stability in a tokamak is the number of complete orbits around the torus a particle completes before returning to its starting point, this number is called the safety factor (q). The bigger the better. We want particles to orbit many times before coming back to where they started, not to spiral around the torus like a phone cord.
The picture below shows q = 2, the title picture above is q=10.
The safety factor describes the geometry the toroidal and poloidal fields. In fact Poincaré maps made by firing electrons at phosphor screens are typically used to determine that the magnets are behaving correctly before plasma experiments can happen.